Question: Simplify the following expression: $ n = \dfrac{x - 5}{3x + 4} + \dfrac{-10}{7} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{x - 5}{3x + 4} \times \dfrac{7}{7} = \dfrac{7x - 35}{21x + 28} $ Multiply the second expression by $\dfrac{3x + 4}{3x + 4}$ $ \dfrac{-10}{7} \times \dfrac{3x + 4}{3x + 4} = \dfrac{-30x - 40}{21x + 28} $ Therefore $ n = \dfrac{7x - 35}{21x + 28} + \dfrac{-30x - 40}{21x + 28} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{7x - 35 - 30x - 40}{21x + 28} $ $n = \dfrac{-23x - 75}{21x + 28}$